Conventionally, an air-fuel ratio control apparatus has been widely known, which comprises a three-way catalytic converter disposed in an exhaust passage (exhaust gas passage) of an internal combustion engine, and an upstream air-fuel ratio sensor and a downstream air-fuel ratio sensor disposed, in the exhaust passage, upstream and downstream of the three-way catalytic converter, respectively. The air-fuel ratio control apparatus calculates, based on the output value of the upstream air-fuel ratio sensor and the output value of the downstream air-fuel ratio sensor, an air-fuel ratio feedback amount, and performs a feedback control on an air-fuel ratio (air-fuel ratio of the engine) of a mixture supplied to the engine in such a manner that the air-fuel ratio of the engine coincides with (becomes equal to) a stoichiometric air-fuel ratio. Further, another air-fuel ratio control apparatus is also proposed, which calculates, based on only one of the output value of the upstream air-fuel ratio sensor and the output value of the downstream air-fuel ratio sensor, an air-fuel ratio feedback amount, and performs a feedback control on the air-fuel ratio of the engine. The air-fuel ratio feedback amount used in these air-fuel ratio control apparatuses is commonly used for all of the cylinders.
Meanwhile, an electronic control fuel injection type internal combustion engine typically comprises at least one fuel injector in each of the cylinders or in each of intake ports, each communicating with each of the cylinders. Accordingly, when a property (characteristic) of the fuel injector for a specific cylinder becomes a “property that the fuel injector injects fuel in an amount larger (more excessive) than an instructed fuel injection amount”, only an air-fuel ratio (air-fuel-ratio-of-the-specific-cylinder) of an air-fuel mixture supplied to the specific cylinder shifts (deviates) to an extremely rich side. That is, a non-uniformity among air-fuel ratios of the cylinders (variation in air-fuel ratios among the cylinders, air-fuel ratio imbalance among the cylinders) becomes high (prominent). In other words, there arises an imbalance among the air-fuel ratios of individual cylinders.
In this case, the average of the air-fuel ratios of the mixtures supplied to the entire engine becomes an air-fuel ratio richer (smaller) than the stoichiometric air-fuel ratio. Accordingly, the feedback amount commonly used for all of the cylinders causes the air-fuel ratio of the specific cylinder to shift to a leaner (larger) air-fuel ratio so that the air-fuel ratio of the specific cylinder is made closer to the stoichiometric air-fuel ratio, and simultaneously, causes each of the air-fuel ratios of the other cylinders to shift to a leaner (larger) air-fuel ratio so that the air-fuel ratios of the other cylinders are made to deviate more from the stoichiometric air-fuel ratio. As a result, the average of the air-fuel ratios of the entire mixtures supplied to the engine is caused to become roughly equal to the stoichiometric air-fuel ratio.
However, the air-fuel ratio of the specific cylinder is still richer (smaller) than the stoichiometric air-fuel ratio, and the air-fuel ratios of the other cylinders become leaner (larger) than the stoichiometric air-fuel ratio, and therefore, a combustion condition of the mixture in each of the cylinders is different from the perfect combustion condition. As a result, an amount of emissions (an amount of unburnt substances and/or an amount of nitrogen oxides) discharged from each of the cylinders increases. Accordingly, even though the average of the air-fuel ratios of the mixtures supplied to the engine coincides with the stoichiometric air-fuel ratio, the three-way catalytic converter may not be able to purify the increased emissions, and thus, there is a possibility that the emissions become worse.
It is therefore important to detect whether or not the air-fuel ratio non-uniformity among cylinders becomes excessively large (the air-fuel ratio imbalance among cylinders is occurring), since an appropriate measure can be taken in order not to worsen the emissions.
One of such conventional apparatuses for determining the air-fuel ratio imbalance among cylinders obtains a trajectory length of the output value (output signal) of an air-fuel ratio sensor (upstream air-fuel ratio sensor described above) disposed at an exhaust gas aggregated portion into which the exhaust gas discharged from the plurality of the cylinders aggregate/merge, compares the trajectory length with a “reference value varying depending on the engine rotational speed and an intake air amount”, and determines, based on the result of the comparison, whether or not the air-fuel ratio imbalance among cylinders is occurring (refer to, for example, U.S. Pat. No. 7,152,594). It should be noted that the determination of whether or not an “excessive air-fuel ratio imbalance among cylinders” has been occurring may be referred to as an “air-fuel ratio imbalance among cylinders determination” or an “imbalance determination”. The “excessive air-fuel ratio imbalance among cylinders” means an air-fuel ratio imbalance among cylinders which causes an amount of unburnt substances or an amount of Nitrogen-oxide to exceed a permissible (tolerable) value.